Figure 6

The attractors and attractor-basin phase portraits for different gain coefficients. Any initial condition is a point in phase space. A square region for possible initial condition in phase space is subdivided into 500 × 500 cells. We perform the iteration and track the points on the grid until the attractors are obtained. Then, we can derive the attractor basin. Different colours correspond to different attractors. (a,c,e and g) are attractor-basin phase portraits for different gain coefficients (g₀); (b,d,f and h) are attractors for (a,c,e and g). For Fig. 6. (a and b), g₀ = 1.7. There are three attractors in (b) (blue, red and green points). The blue point and the red point are stable single-pulse state. The green point indicates no pulse. The attractor basins for the attractors are shown in (a) (use the same colour as the corresponding attractor in (b)) For Fig. 6. (c and d), g₀ = 2.0. There are four attractors in (d) (blue, red, green and yellow points). The blue point and the red point are stable single-pulse states. The green point indicates no pulse. A new attractor (the point with yellow star marker) means that the laser can support 2 pulses under a narrow range of initial conditions. For Fig. 6. (e and f), g₀ = 2.5; There are four attractors in (f) (blue, red, green and yellow points). The blue points and the red points are single-pulse in periodic fluctuation state. The green point indicates no pulse. The yellow point indicates stable double pulses. For Fig. 6. (g and h), g₀ = 3.0; There are three attractors in (h) (blue & dark blue, orange & red, black circle). The blue & dark blue points and the orange & red points are single-pulses in a periodic fluctuation state. The black circle is for double pulses in a periodic fluctuation state.